Question

A particular coal contains 2.55\(\%\) sulfur by mass. When the coal is burned, it produces \(S O_{2}\) emissions, which combine with rainwater to produce sulfuric acid. Use the formula of sulfuric acid to calculate the mass percent of S in sulfuric acid. Then determine how much sulfuric acid (in metric tons) is produced by the combustion of 1.0 metric ton of this coal. ( A metric ton is 1000 \(\mathrm{kg.}\) .

Short answer

Sulfuric acid (H2SO4) has a mass percent of S of approximately 32.69%. The combustion of 1.0 metric ton of coal with 2.55% sulfur content would produce roughly 6.79 metric tons of sulfuric acid.

Step-by-step solution

Calculate the mass of sulfur in 1 metric ton of coal

Use the percentage of sulfur in coal to find the mass of sulfur for 1 metric ton of coal by multiplying the mass of coal by the percentage of sulfur in decimal form.

Calculate the molar mass of sulfur and sulfuric acid

Calculate the molar mass of sulfur (S) and sulfuric acid (H2SO4) using the periodic table to find out how many moles of sulfuric acid can be produced from the sulfur obtained in Step 1.

Determine the mass percent of S in sulfuric acid

Use the molar mass of sulfur and sulfuric acid to calculate the mass percent of S in sulfuric acid by dividing the molar mass of S by the molar mass of H2SO4 and multiplying by 100%.

Convert sulfur mass to moles

Using the molar mass of sulfur, convert the mass of sulfur from Step 1 to moles of sulfur.

Convert moles of sulfur to moles of sulfuric acid

Since the combustion reaction produces one mole of SO2 from one mole of S, and subsequently H2SO4 from SO2, assume a 1:1 mole ratio for the conversion of S to H2SO4.

Convert moles of sulfuric acid to mass

Use the molar mass of sulfuric acid to convert the moles of sulfuric acid from Step 5 to the mass of sulfuric acid.

Convert the mass of sulfuric acid to metric tons

Since the mass of sulfuric acid is calculated in kilograms, convert this mass to metric tons by dividing by 1000 as there are 1000 kilograms in a metric ton.

Key concepts

Mass Percent Calculation

Understanding mass percent is crucial when calculating how much of a specific component is present in a mixture. The mass percent of an element within a compound is determined by the ratio of the mass of that particular element to the total mass of the compound, multiplied by 100 to obtain a percentage. To illustrate, consider the mass percent of sulfur (S) in sulfuric acid (H2SO4). The calculation involves determining the molar mass of sulfur and the molar mass of sulfuric acid.

For sulfur, the molar mass is approximately 32.07 g/mol, and for sulfuric acid, about 98.079 g/mol. The mass percent of sulfur in sulfuric acid would be \(\frac{32.07}{98.079} \times 100\%\), equating to roughly 32.7%. This knowledge allows us to comprehend the proportion of sulfur within sulfuric acid, which is a direct application of mass percent calculation.

Molar Mass Determination

The molar mass of a compound is a fundamental value in stoichiometry, acting as a bridge between the mass of a substance and the amount of substance in moles. It represents the mass of one mole of a substance and is calculated by summing the atomic masses of all atoms in the molecular formula. For example, in sulfuric acid (H2SO4), with hydrogen (H) having a molar mass of approximately 1.01 g/mol, sulfur (S) 32.07 g/mol, and oxygen (O) 16.00 g/mol, the molar mass of sulfuric acid is \(2 \times 1.01 + 32.07 + 4 \times 16.00 = 98.079 g/mol\).

Determining molar mass is essential when converting from moles to grams or vice versa, and it is a key step in solving stoichiometry problems. Recognizing the molar masses of both sulfur and sulfuric acid allows students to convert the mass of sulfur produced from coal combustion into the mass of sulfuric acid.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is based on the law of conservation of mass and the concept of the mole. In simple terms, stoichiometry allows us to predict how much product will form from a given amount of reactant or how much reactant is needed to produce a certain amount of product.

For instance, the combustion of sulfur from coal leads to the formation of sulfur dioxide (SO2), which further reacts with water to form sulfuric acid (H2SO4). Stoichiometry can predict that burning sulfur in an excess of oxygen leads to a 1:1 mole ratio of sulfur to sulfur dioxide, and subsequently one mole of sulfuric acid, under ideal conditions. This relationship is used to convert moles of sulfur to moles of sulfuric acid, which is then translated into mass, addressing questions like 'How much sulfuric acid is produced from 1.0 metric ton of coal containing sulfur?'

Environmental Impact of Sulfur Emissions

The environmental impact of sulfur emissions is a significant concern due to the formation of acid rain. Sulfur dioxide (SO2) released from the combustion of fossil fuels like coal, reacts with water vapor in the atmosphere to form sulfuric acid, which falls as acid rain. Acid rain has detrimental effects on ecosystems, water sources, soil, vegetation, and aquatic life. It can also corrode buildings and infrastructure, leading to economic losses.

By understanding and calculating the amount of sulfuric acid produced through coal combustion, we can estimate the potential impact on the environment. Furthermore, this form of analysis can also contribute to the development of better emission control policies, such as the implementation of scrubbers in smokestacks to reduce sulfur dioxide emissions, or the transition to cleaner energy sources. It underscores the importance of chemistry in addressing environmental challenges posed by industrial processes.